Răspuns:
[tex]f(x)=mx^2+(m-1)x+2m-1[/tex]
[tex]a=m;b=m-1;c=2m-1[/tex]
Ca f(x) sa fie tangenta axei Ox => Delta = 0
[tex]Delta=b^2-4ac[/tex]
[tex]=m^2-2m+1-4m(2m-1)[/tex]
[tex]=m^2-2m+1-8m^2+4m[/tex]
[tex]=-7m^2+2m+1=0[/tex]
Acum avem o ecuatie in m
[tex]m1,m2=\frac{-(-2)+-\sqrt{(-2)^2-4*7*(-1)} }{2*7}=\frac{2+-4\sqrt{2} }{14}[/tex]
[tex]=>m1=\frac{1+2\sqrt{2} }{7}[/tex]
[tex]=> m2=\frac{1-2\sqrt{2} }{7}[/tex]
